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Random Tilings of High Symmetry: I. Mean-Field Theory

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We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, UMR CNRS-UPS 5152, Université Paul Sabatier, 31062, Toulouse Cedex 04, France

    N. Destainville

  2. Department of Physics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    M. Widom

  3. Laboratoire de Physique Théorique des Liquides, Tour 24, Boíte 121, 75252, 4, Place Jussieu, Paris Cedex 05, France

    R. Mosseri

  4. LPSB-CNRS, 92195, Meudon Cedex, France

    F. Bailly

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  1. N. Destainville
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  2. M. Widom
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  3. R. Mosseri
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  4. F. Bailly
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Correspondence to N. Destainville.

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Destainville, N., Widom, M., Mosseri, R. et al. Random Tilings of High Symmetry: I. Mean-Field Theory. J Stat Phys 120, 799–835 (2005). https://doi.org/10.1007/s10955-005-6989-y

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